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Given a n × n matrix A with eigenvalues λ 1 , λ 2 , . . . , λ n , the following result holds.

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(1)

j

i

ij

i

i

j: λ

j6=λi

sλj

sλj−1

i

i

j

i

k

−1

j

i

λj

j

sλj−1

λj

1

j−λi)r

λj

0

j

1

j1

j: λ

j6=λ1

sλj

sλj−1

j

1

k

−1

j

1

λj

j

sλj−1

(2)

λj

λ1r

j

λj

0

1

1

−1

−1

(3)

18

167

(4)

i

i

i

i

j

ij

j

i

(5)

x

kxk2

2

n−1

n−1

2

n−1

i

i

i

(6)

k

n

j=2

j

kj

j

k

n

j=2

j

kj

j

1

k

n

j=2

j

kj

j

T

k

n

j=2

j

kj

j

k

n

j=2

j

kj

j

k

T

n

j=2

j

kj

T

j

n j=2

αj α

λj r

k

j

n j=2

αj α

λj r

k

T

j

j

j

j

j

n j=2

αj α

λj r

k

j

T

j

n j=2

αj α

λj r

k

T

j

n j=2

αj α

λj r

k+1

T

j

n j=2

αj α

λj r

k

T

j

(7)

(8)

2

n

−1

−1

(9)

(10)

(k)i

(11)

(12)

(13)

0

0

1−cc

T

0

term

1

2

k

Berkhin

survey

(14)

j

i

j

i

j

i

j

i

(15)

r+1

r+2

r+3

r+s

r+1

r+2

r+3

r+s

m

2

m

m+1

2

3

m

m+1

12

2

m+2

2

3

4

m

m+1

12

2

m+2

16

3

12

m+32

13

m

m+1

12

2

m+2

m

m+1

m

(16)

j

j

j

j

m

m

m

m+1

m

m+1

12

2

m+2

m

m+1

12

2

m+2

16

3

12

m+32

13

m

s−1

m+s−1

j

1 2

2

2

s−1

s−1

1 2

2

2

s−2

s−2

1 2

2

2

1

6

3

12

2

13

3

s−1

s−1

j

1

j

1

j

1

j

1

m1

j

1

j

1

j

1

(17)

m

1 2

2

2

1

6

3

12

2

13

3

s−1

s−1

1 2

2

2

s−2

s−2

m

1 2

2

2

1

6

3

12

2

13

3

s−1

s−1

.

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